9_rolling element bearings.pdf
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ROLLING ELEMENT
BEARING
Antifriction Bearing
ABMA (American Bearing
Manufacturers Association) AFBMA (Anti-friction Bearing
Manufacturers Association)
TIMKEN, SKF
Is a precision item and can not be “Designed” but only “Selected” out of available ones!
M S Dasgupta, BITS Pilani
Unlike coefficient of sliding friction, the coefficient of rolling friction varies with conditions and has a dimension as unit of length. The rolling resistance can be expressed as Fr = c W (1) where Fr = rolling friction (N) c = rolling resistance coefficient - dimensionless (coefficient of rolling friction - CRF) W = m g = normal force or weight of body (N) m = mass of body (kg) g = accelaration of gravity (9.81 m/s2) The rolling resistance can alternatively be expressed as Fr = cl W / r (2) where cl = rolling resistance coefficient with dimension length (coefficient of rolling friction) (mm) r = radius of wheel (mm)
M S Dasgupta, BITS Pilani
Size?
Advantage?
Although the starting friction is about twice the
running friction, but still it is negligible in
comparison with the starting friction of a journal
bearing
Working
M S Dasgupta, BITS Pilani
Rolling elements
Single use item
M S Dasgupta, BITS Pilani
Ball Bearing Nomenclature:
Conrad type
Filling Notch type
How the balls go inside the races?
M S Dasgupta, BITS Pilani
Balls / Rollers as rolling element
One piece cage retainer
Different types of ball bearings:
Different types of roller bearings
a) Straight roller
b) Tapered roller, thrust
c) Spherical roller, thrust
d) Needle
e) Tapered roller (both radial and thrust)
f) Steep-angle tapered roller
Bearing life
•Virtually infinite!
• If maintained in condition of clean and properly lubricated,
is mounted and sealed against the entrance of dust and dirt
and is operated at reasonable temperatures, then metal
fatigue will be the only cause of failure.
•For example Timken company takes the failure criterion as
a wear area of 6.45 mm2.
•Wear debris, vibration etc. may be other criteria.
•Bearing life of an individual bearing is defined as the total
number of revolutions (or hours at a constant speed) of
bearing operation until the failure criterion is developed.
Rating life
•The rating life is used by AFBMA (Anti-friction Bearing
Manufacturers Association)
• “the rating life of a group of nominally identical ball or
roller bearings is defined as the number of revolutions (or
hours at a constant speed) that 90% of the group of bearings
will achieve or exceed before the failure criterion develops.”
• Rating life for different manufacturers:
SKF : 106 revolutions
Timken : 90(10)6 revolutions
Bearing load (F) - Life (L) trade-off at
constant (rated, 90%) reliability (R):
Rating Life
Fig: Typical bearing load-life log-log curve.
Using a regression equation of the form
Experimentally obtained data plotted, for 90% reliability
a
DDD
a
RR nFnC/1/1
10 6060
aa LFLF1
22
1
11
Associating the load F1 with C10, the catalogue rating that you need to look at, and
the life measure in revolutions L1 with the L10, which is the manufacturer specific
quantity, FD and LD refer to the design quantities for the bearing to be selected, we
can write,
a
DD
aLFLC
/1/1
1010
Here If we want to specify in the life hours, then we can write, rpm (nR & nD) values:
Rating
Life=L10
Desired
Life=LD
Desired Load=FD
Rating Load=C10
1
2
Bearing load (F) - Life (L) trade-off at
constant (rated, 90%) reliability (R):
a
DDD
a
RR nFnC/1/1
10 6060
Catalog rating, kN
Rating life in hours
Rating speed in RPM Desired load, kN
Desired life in hours
Desired speed in RPM
Solving for C10 gives
a
DDD
a
RR
DDD
liferating
nF
nL
nF
/1/1
10
60
60
60 Crating, load Catalogue
Bearing load (F) - Life (L) trade-off at
constant (rated, 90%) reliability (R):
M S Dasgupta, BITS Pilani
The Desired load (FD) is not steady then Load application factor
(A.F) is used
Table 11–5
Effect of load application factor
Table 11–3
Dimensions and Basic Load Ratings for
Cylindrical Roller Bearings
The coding method for standard bearings:
As per ABMA, the bearings are identified by a two-digit number
called the dimension-series code.
The first number is from the width series, 0, 1, 2, 3, 4, 5, & 6.
The second number is from the diameter series (outside), 8, 9, 0, 1, 2,
3, & 4.
Table 11–2:
Dimensions and Load Ratings for Single-Row 02-Series
Deep-Groove and Angular-Contact Ball Bearings
Shoulder dimensions:
What ds and dH in the catalogues
mean…
The housing and shaft shoulder diameters
listed in the tables should be used whenever
possible to secure adequate support for the
bearing and to resist the maximum thrust
loads
Reliability goal of the mechanical system
• The combined reliability goal is normally specified, say, Rt.
• Then each of the two bearings, if both of them are same type, must possess a reliability of:
t
t
t
tBA
BAt
RRThus
R
Rge
RRor
RRRRRRRIf
RRR
,
948.090.0
,90.0.,.
, 2
When dissimilar bearings are to be chosen at the two ends, the more
critical of the two will be designed for Rt. RB=Rt/RA=Rt/Rt=1. Thus
automatically the second bearing will have 100% reliability.
0
0
exp[ ( ) ]bx xR
x
Using the Weibull distribution, along any
constant load line (horizontal line in the
graph):
=characteristic parameter corresponding to the 63.2121 percentile value of the
variate; b= shape parameter that controls the skewness
Bearing load (F) - Life (L) - reliability (R)
three-way relationship
(What to do, if more than 90% reliability is desired?):
R=reliability
x=life measure dimensionless variate, L/L10
x0=guaranteed, or minimum value of the variate
1/
10 1/
0 0
( ) , 0.90( )(1 )
aDD b
D
xC F R
x x R
aDD
aBB xFxF
11
a
B
aD
DB
x
xFF
1
1
Along a constant load line (AB),
ngsubstituti
Rxxx
xSolving
x
xxR
b
D
B
B
b
BD
/1
00
0
0
1ln
exp
a
b
D
DD
aB
aD
DBRxx
xF
x
xFCF
/1
/1
00
1
1
10/1ln
The natural logarithmic function can be series-expanded and simplified to yield
Bearing load (F) - Life (L) - reliability (R)
three-way relationship
Accounting for thrust force:
1e
r
F
VF when
e a
r r
F FX Y
VF VF when
e i r i aF X VF Y F
Purpose is to find the equivalent radial load Fe, that
would do the same damage as that done by the
existing radial and thrust loads together. V is the
rotation factor. V=1 for inner ring rotation, V=1.2
for outer ring rotation.
e Generalizing for both zones,
For horizontal line zone, i=1 and for inclined line zone, i=2.
Table 11-1 gives the values of Xi and Yi.
a
a
Fe may separately be multiplied by ‘service factor’ if load is not steady
Table 11–1
Equivalent Radial Load Factors for Ball Bearings
Variable loading:
= Constant = K a
F L
F may be already be an equivalent
steady radial load for radial-thrust load
combination If load level of F1 is selected and run to failure
criteria, the area under the F1- L1 trace is
numerically equal to K
Three types of variable loading are possible:
1) Piecewise constant loading in a cycle pattern
2) Continuously variable loading in a repeatable cyclic pattern
3) Random variation
The damage done by loads Fe1, Fe2, and Fe3 is
D = Fae1 l1 + Fa
e2 l2 + Fae3 l3
The loads Fei are equivalent steady radial loads for combined radial–thrust loads.
The equivalent steady load Feq
when run for l1 + l2 + l3 revolutions
does the same damage D.
Thus
D = Faeq (l1 + l2 + l3)
Equating above equations and solving for Feq
Piece-wise continuous cycle:
Piece-wise continuous cycle:
1/{ [( ) ] }a a
eq i i eiF f AF F
li can be expressed as ni ti , where ni is the rotational speed at load Fei and ti is the duration of that speed,
1/ 1/1 1 2 2 3 3
1 2 3
[ ] [ ]a a a
a a a
eq i i
F l F l f lF f F
l l l
1/[ ]
a
i i ei a
eq
i i
n t FF
n t
where fi is the fraction of revolution run up under load Fei .
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